WELL- AND ILL-POSEDNESS ISSUES FOR ENERGY SUPERCRITICAL WAVES

被引：16

作者：

Ibrahim, Slim ^{[1
]}

Majdoub, Mohamed ^{[2
]}

Masmoudi, Nader ^{[3
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8P 5C3, Canada

[2] Univ Tunis El Manar, Dept Math, Tunis 2092, Tunisia

[3] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

ANALYSIS & PDE | 2011年 / 4卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

nonlinear wave equation; well-posedness; ill-posedness; finite speed of propagation; oscillating second order ODE; KLEIN-GORDON EQUATIONS; GLOBAL CAUCHY-PROBLEM; SOBOLEV SPACE; REGULARITY; INEQUALITY; UNIQUENESS; INSTABILITY; SCATTERING; EXISTENCE;

D O I：

10.2140/apde.2011.4.341

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. The proof uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation. We also obtain some ill-posedness and weak ill-posedness results.

引用

页码：341 / 367

页数：27

共 49 条

[1] Trudinger type inequalities in RN and their best exponents [J].